2009 Vol. 30, No. 10

Display Method:
Thermoelastic Analysis of a Functionally Graded Annulus With an Arbitrary Gradient
PENG Xu-long, LI Xian-fang
2009, 30(10): 1135-1142. doi: 10.3879/j.issn.1000-0887.2009.10.001
Abstract(1058) PDF(745)
A thermoelastic problem of a circular annulus made of functionally graded materials with an arbitrary gradient was investigated. Different from previous works, the analysis neither requires a special form of the gradient of material properties nor demands to partition the entire structure into a multilayered homogeneous structure. Instead, a new method for solving the thermoelastic problem of a functionally graded circular annulus by transforming it to a Fredholm integral equation was proposed. The distribution of thermal stresses and radial displacement could be obtained by the solution to the resulting equation. Finally, illustrative examples were given to show the effects of varying gradients on the thermal stresses and radial displacement for given temperature changes at the inner and outer surfaces. Obtained results indicate that the thermal stresses can be relaxed for specified gradients, which is of benefit to designing a nonhomogeneous annulus to maintain structural integrity.
Interaction Between a Heat Dipole and a Circular Interfacial Crack
XIAO Wan-shen, XIE Chao, LIU You-wen
2009, 30(10): 1143-1152. doi: 10.3879/j.issn.1000-0887.2009.10.002
Abstract(1319) PDF(724)
The heat dipole consists of a heat source and a heatsink. The problem that an interfacial crack of a composite contains a circular inclusion under a heat dipole is investigated by using the analytic extension technique, generalized Liouville's theorem and Muskhelishvili boundary value theory. Temperature fields and stress fields are formulated, and then the effects of the temperature field and the inhomogeneity on the interfacial fracture are analyzed. As a numerical illustration, the thermal stress intensity factors of the in terfacial crack are presented for various material combinations and for different positions of the heat dipole. The characteristic of the in terfacial crack depends on the elasticity, thermal property of the composite and the condition of the dipole.
A Novel Virtual Node Method for Polygonal Elements
TANG Xu-hai, WU Sheng-chuan, ZHENG Chao, ZHANG Jian-hai
2009, 30(10): 1153-1164. doi: 10.3879/j.issn.1000-0887.2009.10.003
Abstract(1254) PDF(929)
A novel polygonal finite element method (PFEM), which is based on partition of unity, was proposed and named as virtual node method (VNM). To test the perform ance of present method, intensive numerical examples were carried out for solid mechanic problems. With polynomial form, virtual node method achieves better results than that of traditional PFEM, including Wachspress method and mean value method in standard patch test Compared with standard triangular FEM, virtual node method can achieve better accuracy. With the ability to construct shape function on polygonal elements, virtual node method provides greater flexibility in mesh generation. Therefore, several fracture problems were studied to demonstrate poten tialim plemen tation. With the advantage of virtual node method, convenien trefinement and remeshing strategy are applied.
Numerical Simulation of Solid Tumor Angiogenesis With Endostatin Treatment: a Combined Analysis of Anti-Angiogenic Factor Inhibiting Effect and Extra-Cellular Matrix Micro Mechanical Environment
CAI Yan, WU Jie, Kalkabay Gulnar, ZHANG Hong-yi, CAO Jin-feng, XU Shi-xiong, Quan Long, M. W. Collins
2009, 30(10): 1165-1172. doi: 10.3879/j.issn.1000-0887.2009.10.004
Abstract(1412) PDF(792)
To investigate the in fluence of anti-angiogenesis drug Endostatin to solid tumor angiogenesis, a mathe matical model of tumor angiogenesis was developed with combined influences of local extra-cellular matrix mechanical environment, and the inhibiting effects of Angiostatin and Endostatin. The simulation results show that Angiostat in and Endostatin caneffectively inhibit the process of tumor angiogenesis, and decrease the number of blood vessels in the tumor. The present model could be used as a valid theoreticalm ethod in the investigation of anti-angiogenic therapy of tumors.
Series Solutions for the Stagnation Flow of a Second Grade Fluid Over a Shrinking Sheet
S. Nadeem, Anwar Hussain, M. Y. Malik, T. Hayat
2009, 30(10): 1173-1180. doi: 10.3879/j.issn.1000-0887.2009.10.005
Abstract(1156) PDF(638)
The analytic solutions of boundary layer flows bounded by a shrinking sheet are derived. Using similarity transformations, the partial differential equations were reduced into the ordinary differen tial equations which were then solved by homotopy analysis method (HAM). Two-dimen sional and axisymmetric shrinking flow cases were discussed.
Space-Time Objective Decomposition of the Vortex Equations and the Mechanism Analysis of the Subtropical High Abnormal Activities
HONG Mei, ZHANG Ren, XUE Feng, LIU Ke-feng
2009, 30(10): 1181-1188. doi: 10.3879/j.issn.1000-0887.2009.10.006
Abstract(1015) PDF(724)
Inorder to analyze the dynamic mechanism of unusual activities of the subtropical high, based on the heat force and the whorlmovement dissipation effect, the partial differential vortex equations were space-time variable separated by Galerkin methods. Aiming at the subjective and man-made conven tionalmethod of choice in the space-based function, the research ideas of the EOF and the genetic algorithm combined inversion of the space-based functions from the actual sequence of fields were putforward. Agroup of trigonometric functions were chosen as a broad-space based function, with the leas-tsquares of the error of the based function and EOF typical fields, as well as the complete orthogonal conformation of based functions as the dualbound function. Then, the genet ic algorithm w as introduced to carry out the surface fitting and coefficientop timization of the based function, as aresul't the objective and reasonable constant differen tial equation of the subtropical high was obtained by inversion. Finally, based on the obtained nonlinear dynamics model the dynamic behavior and mechanism of the sub tropical high was analyzed and discussed under the in fluence of heat force. It is found that solar radiation heating and zonal differences in land and seamipacting the potential field and flow field changes of the sub-tropical areas are the miportant factors that canlead to the strength changes of the subtropical high and medium-term advance and retreat activities. The frontis gradual change, while the lastmore putup the characteristic of the break. Some meaning fulresults were gotthrough the analysis.
Topographic Effects on Polar Low and Tropical Cyclone Development in a Simple Theoretical Model
LI Zi-liang, FU Gang, GUO Jing-tian, DUAN Yi-hong, ZHANG Mei-gen
2009, 30(10): 1189-1201. doi: 10.3879/j.issn.1000-0887.2009.10.007
Abstract(1072) PDF(738)
The polar low and tropical cyclone type vortices over topography are assumed to beaxial-symmetrical and thermal wind balanced systems, which are solved as aninitial value problem of linearized vortex equation set in cylindrical coord inates. The roles of sensible and latent heating, friction and topography on the structure and intensification of polar low and tropical cyclone type vortices were an alyzed. The radial velocity, vertical velocity, azmiuthal velocity and the unstable growth rate including the topography effects are obtained. It is shown that the in teraction between flow and topography plays a significantrole for the structure and intens ification of polar low and tropical cyclone system. Analys is of the topography term indicate that in the up-slope side of the mountain, the radial in flow and the verticalascent forced by the mountain will in tensify the polar low and tropical cyclone type vortex and increase the unstable growthrate. However, in the lee side of the mountain, the radial inflow and the vertical descent forced by the mountain will weaken the polar low and tropical cyclone type vortex and decrease the unstable growth rate of polar low and tropical cyclone system. In addition, the evolutionary process and spatial structure of the polar low observed over the Japan Sea on 19 December 2003 were investigated by using observational data to verify this theoretical result.
Recursive Lagrangian Dynamic Modeling and Simulation of Multi-Link Spatial Flexible Manipulator Arms
ZHANG Ding-guo
2009, 30(10): 1202-1212. doi: 10.3879/j.issn.1000-0887.2009.10.008
Abstract(1285) PDF(2257)
The dynamics for multi-link spatial flexible manipulatorarm sconsisting of nlinks andnrotary joints is investigated Kinematics of both the rotaryjoint motion and the link deformation were described by 4×4 homogenous transformation matrices, and the Lagrangian equations were used to derive the governing equations of motion of the system. In the modeling the recursive strategy for kinematics was adopted to improve the computational efficiency. Both the bending and torsional flexibility of the link were taken in to account. Based on the presented method a general-purpose soft ware package for dynamic smiulation was developed. To validate the algorithm presented, the dynamic simulation of a spatial flexible manipulatorarm was given as anexample.
A New Modal Identification Method Under the Non-Stationary Gaussian Ambient Excitation
DU Xiu-li, WANG Feng-quan
2009, 30(10): 1213-1222. doi: 10.3879/j.issn.1000-0887.2009.10.009
Abstract(1126) PDF(875)
Based on the multivariate continuous tmie autoregressive model, a new time-domain modal identification method of LTI system driven by the uniformly modulated Gaussian random excitation was presented. The method canidentify the physical parameters of the system from the response data. First, the structural dynamic equation is transformed into the continuous tmie autoregressive model of order 3. Second, based on the assumption that the uniformly modulated function is approx miately equal to a constant matrix in a very short time period and the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise, an d two special situations are discussed too. Finally, by virtue of the Girsanov theorem, a likelihood function was in troduced, which is just a conditional density function. Maxmiizing the likelihood function gives the exact maximum likelihood estmiators of model parameters. Numerical results show that the method has high precision and computing efficiency.
Heterogeneous Boundedly Rational Expectation Model for Housing Market
LEUNG Andrew Y T, XU Jia-na, TSUI Wing-shum
2009, 30(10): 1223-1233. doi: 10.3879/j.issn.1000-0887.2009.10.010
Abstract(1110) PDF(766)
The housing price dynamics was tested when considering heterogeneous boundedly rational expectations, such as naive expectation, adaptive expectation and biased belief. Housing market was investigated as an evolutionary system with heterogeneous and competing expectations. The results show that the dynamics of the expected housing pricevaries substantially when heterogeneous expectations are considered together with some other endogenous factors. The simulation results explain some stylized phenomena, such as equilibrium or oscillation, convergence or divergence, and over-shooting or under-shooting. Furthermore, the results suggest that the variation of the proportion of each group of the agents is basically dependent on the selected strategies. It is indicated that control policies should be chosen carefully in consistence with a uniquereal estate market during a unique period since some certain parameters portfolio mayincrease or suppress the oscillation.
Asymptotic Stability for Impulsive Functional Differential Equations
LUO Zhi-guo, LUO Yan
2009, 30(10): 1234-1242. doi: 10.3879/j.issn.1000-0887.2009.10.011
Abstract(1032) PDF(714)
The stability for aclass of mipulsive functional differential equation was inve stigated. By improving the upper bound of Lia punovfunctional and based on the application of the Liapunov second method to gether with Liapunov functional and Jensencs the inequality, auniformly stability theorem and auniformly asymptotically stability theorems are obtained. Examples are also given to demonstrate the a dvantage of our results.
Numerical Solution of Poisson Equation by Using Wavelet Bases of Hermite Cubic Splines on the Interval
XIANG Jia-wei, CHEN Xue-feng, LI Xi-kui
2009, 30(10): 1243-1250. doi: 10.3879/j.issn.1000-0887.2009.10.012
Abstract(1461) PDF(698)
A new wavelet-based finite element method was proposed for solving Poisson equation. The wave let bases of Hermite cubic splines on the in terval were employed as the multi-scale in terpo lating basis for finite element analysis. The lifting scheme of wavele-tbased finite element method was discussed in details. For the orthogral characteristic of the wavelet bases with respect to the given inner product, the correspond ing multi-scale finite element equation will be decoupled across scales to tally or partially and be suited for nesting approx mi ation. Some num erica l exam p les ind icate that the p roposed method has higher efficiency and precision in solving Poisson equation.
Eventually Vanished Solutions of a Forced Li閚ard System
ZHANG Yong-xin
2009, 30(10): 1251-1260. doi: 10.3879/j.issn.1000-0887.2009.10.013
Abstract(913) PDF(659)
Eventually vanished solutions, a special class of bounded solutions which tend to 0→±∞, of a Linard system with a tmie-dependent force were found. Not assuming it to be a small perturbation of a Hamiltonian system, the well-known Melnikov method could not be employed to determine the existence of eventually vanished solutions. A sequence of periodically forced systems was applied to approximate the considered system and their periodic solutions were found, where the difficulties caused by the non-Hamiltonian form were overcome by applying the Schaudercs fixed point theorem. The fact that the sequence of those periodic solutions has an accumulation gave the existence of an eventually vanished solution of the forced Linard system.